LMFDB - Embedded newform 430.2.b.a.259.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(259,430)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("430.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			259.2
Root			$1.45161 + 1.45161i$ of defining polynomial
Character	$\chi$	$=$	430.259
Dual form			430.2.b.a.259.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -0.688892i q^{3} -1.00000 q^{4} +(0.311108 + 2.21432i) q^{5} -0.688892 q^{6} -1.90321i q^{7} +1.00000i q^{8} +2.52543 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -0.688892i q^{3} -1.00000 q^{4} +(0.311108 + 2.21432i) q^{5} -0.688892 q^{6} -1.90321i q^{7} +1.00000i q^{8} +2.52543 q^{9} +(2.21432 - 0.311108i) q^{10} +0.214320 q^{11} +0.688892i q^{12} -5.42864i q^{13} -1.90321 q^{14} +(1.52543 - 0.214320i) q^{15} +1.00000 q^{16} -0.0666765i q^{17} -2.52543i q^{18} +7.90321 q^{19} +(-0.311108 - 2.21432i) q^{20} -1.31111 q^{21} -0.214320i q^{22} -4.21432i q^{23} +0.688892 q^{24} +(-4.80642 + 1.37778i) q^{25} -5.42864 q^{26} -3.80642i q^{27} +1.90321i q^{28} -0.592104 q^{29} +(-0.214320 - 1.52543i) q^{30} +3.64296 q^{31} -1.00000i q^{32} -0.147643i q^{33} -0.0666765 q^{34} +(4.21432 - 0.592104i) q^{35} -2.52543 q^{36} +2.02074i q^{37} -7.90321i q^{38} -3.73975 q^{39} +(-2.21432 + 0.311108i) q^{40} -10.6128 q^{41} +1.31111i q^{42} -1.00000i q^{43} -0.214320 q^{44} +(0.785680 + 5.59210i) q^{45} -4.21432 q^{46} +7.59210i q^{47} -0.688892i q^{48} +3.37778 q^{49} +(1.37778 + 4.80642i) q^{50} -0.0459330 q^{51} +5.42864i q^{52} +8.57628i q^{53} -3.80642 q^{54} +(0.0666765 + 0.474572i) q^{55} +1.90321 q^{56} -5.44446i q^{57} +0.592104i q^{58} +2.23506 q^{59} +(-1.52543 + 0.214320i) q^{60} -11.3620 q^{61} -3.64296i q^{62} -4.80642i q^{63} -1.00000 q^{64} +(12.0207 - 1.68889i) q^{65} -0.147643 q^{66} -15.6430i q^{67} +0.0666765i q^{68} -2.90321 q^{69} +(-0.592104 - 4.21432i) q^{70} +6.16839 q^{71} +2.52543i q^{72} +15.2558i q^{73} +2.02074 q^{74} +(0.949145 + 3.31111i) q^{75} -7.90321 q^{76} -0.407896i q^{77} +3.73975i q^{78} +2.93332 q^{79} +(0.311108 + 2.21432i) q^{80} +4.95407 q^{81} +10.6128i q^{82} +8.18913i q^{83} +1.31111 q^{84} +(0.147643 - 0.0207436i) q^{85} -1.00000 q^{86} +0.407896i q^{87} +0.214320i q^{88} +15.9605 q^{89} +(5.59210 - 0.785680i) q^{90} -10.3319 q^{91} +4.21432i q^{92} -2.50961i q^{93} +7.59210 q^{94} +(2.45875 + 17.5002i) q^{95} -0.688892 q^{96} +2.06668i q^{97} -3.37778i q^{98} +0.541249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9	$ 6 q - 6 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9} - 12 q^{11} + 2 q^{14} - 4 q^{15} + 6 q^{16} + 34 q^{19} - 2 q^{20} - 8 q^{21} + 4 q^{24} - 2 q^{25} - 6 q^{26} + 10 q^{29} + 12 q^{30} - 18 q^{31} + 12 q^{35} - 2 q^{36} + 4 q^{39} - 10 q^{41} + 12 q^{44} + 18 q^{45} - 12 q^{46} + 20 q^{49} + 8 q^{50} - 40 q^{51} + 4 q^{54} - 2 q^{56} - 40 q^{59} + 4 q^{60} - 42 q^{61} - 6 q^{64} + 32 q^{65} + 12 q^{66} - 4 q^{69} + 10 q^{70} - 16 q^{71} - 28 q^{74} + 32 q^{75} - 34 q^{76} + 18 q^{79} + 2 q^{80} - 10 q^{81} + 8 q^{84} - 12 q^{85} - 6 q^{86} + 28 q^{89} + 20 q^{90} - 22 q^{91} + 32 q^{94} + 2 q^{95} - 4 q^{96} + 16 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9 - 12 * q^11 + 2 * q^14 - 4 * q^15 + 6 * q^16 + 34 * q^19 - 2 * q^20 - 8 * q^21 + 4 * q^24 - 2 * q^25 - 6 * q^26 + 10 * q^29 + 12 * q^30 - 18 * q^31 + 12 * q^35 - 2 * q^36 + 4 * q^39 - 10 * q^41 + 12 * q^44 + 18 * q^45 - 12 * q^46 + 20 * q^49 + 8 * q^50 - 40 * q^51 + 4 * q^54 - 2 * q^56 - 40 * q^59 + 4 * q^60 - 42 * q^61 - 6 * q^64 + 32 * q^65 + 12 * q^66 - 4 * q^69 + 10 * q^70 - 16 * q^71 - 28 * q^74 + 32 * q^75 - 34 * q^76 + 18 * q^79 + 2 * q^80 - 10 * q^81 + 8 * q^84 - 12 * q^85 - 6 * q^86 + 28 * q^89 + 20 * q^90 - 22 * q^91 + 32 * q^94 + 2 * q^95 - 4 * q^96 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	0.688892i		−	0.397732i	−0.980027	−	0.198866i	$-0.936274\pi$
$3$		−	0.688892i		−	0.397732i	0.980027	−	0.198866i	$-0.0637259\pi$
$4$	−1.00000			−0.500000
$5$	0.311108	+	2.21432i	0.139132	+	0.990274i
$5$	0.311108	+	2.21432i	0.139132	+	0.990274i
$6$	−0.688892			−0.281239
$7$		−	1.90321i		−	0.719346i	−0.933078	−	0.359673i	$-0.882888\pi$
$7$		−	1.90321i		−	0.719346i	0.933078	−	0.359673i	$-0.117112\pi$
$8$			1.00000i			0.353553i
$9$	2.52543			0.841809
$10$	2.21432	−	0.311108i	0.700229	−	0.0983809i
$11$	0.214320			0.0646198			0.0323099	−	0.999478i	$-0.489714\pi$
$11$	0.214320			0.0646198			0.0323099	+	0.999478i	$0.489714\pi$
$12$			0.688892i			0.198866i
$13$		−	5.42864i		−	1.50563i	−0.658230	−	0.752817i	$-0.728695\pi$
$13$		−	5.42864i		−	1.50563i	0.658230	−	0.752817i	$-0.271305\pi$
$14$	−1.90321			−0.508655
$15$	1.52543	−	0.214320i	0.393864	−	0.0553371i
$16$	1.00000			0.250000
$17$		−	0.0666765i		−	0.0161714i	−0.999967	−	0.00808572i	$-0.997426\pi$
$17$		−	0.0666765i		−	0.0161714i	0.999967	−	0.00808572i	$-0.00257379\pi$
$18$		−	2.52543i		−	0.595249i
$19$	7.90321			1.81312			0.906561	−	0.422076i	$-0.138698\pi$
$19$	7.90321			1.81312			0.906561	+	0.422076i	$0.138698\pi$
$20$	−0.311108	−	2.21432i	−0.0695658	−	0.495137i
$21$	−1.31111			−0.286107
$22$		−	0.214320i		−	0.0456931i
$23$		−	4.21432i		−	0.878746i	−0.898305	−	0.439373i	$-0.855201\pi$
$23$		−	4.21432i		−	0.878746i	0.898305	−	0.439373i	$-0.144799\pi$
$24$	0.688892			0.140620
$25$	−4.80642	+	1.37778i	−0.961285	+	0.275557i
$26$	−5.42864			−1.06464
$27$		−	3.80642i		−	0.732547i
$28$			1.90321i			0.359673i
$29$	−0.592104			−0.109951			−0.0549755	−	0.998488i	$-0.517508\pi$
$29$	−0.592104			−0.109951			−0.0549755	+	0.998488i	$0.517508\pi$
$30$	−0.214320	−	1.52543i	−0.0391293	−	0.278504i
$31$	3.64296			0.654295			0.327147	−	0.944973i	$-0.393913\pi$
$31$	3.64296			0.654295			0.327147	+	0.944973i	$0.393913\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	0.147643i		−	0.0257014i
$34$	−0.0666765			−0.0114349
$35$	4.21432	−	0.592104i	0.712350	−	0.100084i
$36$	−2.52543			−0.420905
$37$			2.02074i			0.332208i	0.986108	+	0.166104i	$0.0531188\pi$
$37$			2.02074i			0.332208i	−0.986108	+	0.166104i	$0.946881\pi$
$38$		−	7.90321i		−	1.28207i
$39$	−3.73975			−0.598839
$40$	−2.21432	+	0.311108i	−0.350115	+	0.0491905i
$41$	−10.6128			−1.65745			−0.828724	−	0.559657i	$-0.810933\pi$
$41$	−10.6128			−1.65745			−0.828724	+	0.559657i	$0.810933\pi$
$42$			1.31111i			0.202308i
$43$		−	1.00000i		−	0.152499i
$43$		−	1.00000i		−	0.152499i
$44$	−0.214320			−0.0323099
$45$	0.785680	+	5.59210i	0.117122	+	0.833622i
$46$	−4.21432			−0.621368
$47$			7.59210i			1.10742i	0.832709	+	0.553711i	$0.186789\pi$
$47$			7.59210i			1.10742i	−0.832709	+	0.553711i	$0.813211\pi$
$48$		−	0.688892i		−	0.0994330i
$49$	3.37778			0.482541
$50$	1.37778	+	4.80642i	0.194848	+	0.679731i
$51$	−0.0459330			−0.00643190
$52$			5.42864i			0.752817i
$53$			8.57628i			1.17804i	0.808117	+	0.589022i	$0.200487\pi$
$53$			8.57628i			1.17804i	−0.808117	+	0.589022i	$0.799513\pi$
$54$	−3.80642			−0.517989
$55$	0.0666765	+	0.474572i	0.00899066	+	0.0639913i
$56$	1.90321			0.254327
$57$		−	5.44446i		−	0.721136i
$58$			0.592104i			0.0777471i
$59$	2.23506			0.290980			0.145490	−	0.989360i	$-0.453524\pi$
$59$	2.23506			0.290980			0.145490	+	0.989360i	$0.453524\pi$
$60$	−1.52543	+	0.214320i	−0.196932	+	0.0276686i
$61$	−11.3620			−1.45475			−0.727375	−	0.686240i	$-0.759260\pi$
$61$	−11.3620			−1.45475			−0.727375	+	0.686240i	$0.759260\pi$
$62$		−	3.64296i		−	0.462656i
$63$		−	4.80642i		−	0.605552i
$64$	−1.00000			−0.125000
$65$	12.0207	−	1.68889i	1.49099	−	0.209481i
$66$	−0.147643			−0.0181736
$67$		−	15.6430i		−	1.91109i	−0.294843	−	0.955546i	$-0.595267\pi$
$67$		−	15.6430i		−	1.91109i	0.294843	−	0.955546i	$-0.404733\pi$
$68$			0.0666765i			0.00808572i
$69$	−2.90321			−0.349506
$70$	−0.592104	−	4.21432i	−0.0707700	−	0.503708i
$71$	6.16839			0.732053			0.366026	−	0.930604i	$-0.380718\pi$
$71$	6.16839			0.732053			0.366026	+	0.930604i	$0.380718\pi$
$72$			2.52543i			0.297624i
$73$			15.2558i			1.78556i	0.450496	+	0.892779i	$0.351247\pi$
$73$			15.2558i			1.78556i	−0.450496	+	0.892779i	$0.648753\pi$
$74$	2.02074			0.234907
$75$	0.949145	+	3.31111i	0.109598	+	0.382334i
$76$	−7.90321			−0.906561
$77$		−	0.407896i		−	0.0464841i
$78$			3.73975i			0.423443i
$79$	2.93332			0.330025			0.165012	−	0.986292i	$-0.447234\pi$
$79$	2.93332			0.330025			0.165012	+	0.986292i	$0.447234\pi$
$80$	0.311108	+	2.21432i	0.0347829	+	0.247568i
$81$	4.95407			0.550452
$82$			10.6128i			1.17199i
$83$			8.18913i			0.898874i	0.893312	+	0.449437i	$0.148375\pi$
$83$			8.18913i			0.898874i	−0.893312	+	0.449437i	$0.851625\pi$
$84$	1.31111			0.143054
$85$	0.147643	−	0.0207436i	0.0160142	−	0.00224996i
$86$	−1.00000			−0.107833
$87$			0.407896i			0.0437310i
$88$			0.214320i			0.0228466i
$89$	15.9605			1.69181			0.845906	−	0.533332i	$-0.179060\pi$
$89$	15.9605			1.69181			0.845906	+	0.533332i	$0.179060\pi$
$90$	5.59210	−	0.785680i	0.589460	−	0.0828180i
$91$	−10.3319			−1.08307
$92$			4.21432i			0.439373i
$93$		−	2.50961i		−	0.260234i
$94$	7.59210			0.783066
$95$	2.45875	+	17.5002i	0.252263	+	1.79549i
$96$	−0.688892			−0.0703098
$97$			2.06668i			0.209839i	0.994481	+	0.104920i	$0.0334585\pi$
$97$			2.06668i			0.209839i	−0.994481	+	0.104920i	$0.966541\pi$
$98$		−	3.37778i		−	0.341208i
$99$	0.541249			0.0543976
$100$	4.80642	−	1.37778i	0.480642	−	0.137778i
$101$	−7.60639			−0.756865			−0.378432	−	0.925629i	$-0.623537\pi$
$101$	−7.60639			−0.756865			−0.378432	+	0.925629i	$0.623537\pi$
$102$			0.0459330i			0.00454804i
$103$		−	5.18421i		−	0.510815i	−0.966833	−	0.255408i	$-0.917790\pi$
$103$		−	5.18421i		−	0.510815i	0.966833	−	0.255408i	$-0.0822097\pi$
$104$	5.42864			0.532322
$105$	−0.407896	−	2.90321i	−0.0398066	−	0.283324i
$106$	8.57628			0.833002
$107$			16.9748i			1.64102i	0.571634	+	0.820508i	$0.306310\pi$
$107$			16.9748i			1.64102i	−0.571634	+	0.820508i	$0.693690\pi$
$108$			3.80642i			0.366273i
$109$	−9.47949			−0.907971			−0.453985	−	0.891009i	$-0.649998\pi$
$109$	−9.47949			−0.907971			−0.453985	+	0.891009i	$0.649998\pi$
$110$	0.474572	−	0.0666765i	0.0452487	−	0.00635736i
$111$	1.39207			0.132130
$112$		−	1.90321i		−	0.179837i
$113$		−	1.82225i		−	0.171422i	−0.996320	−	0.0857112i	$-0.972684\pi$
$113$		−	1.82225i		−	0.171422i	0.996320	−	0.0857112i	$-0.0273162\pi$
$114$	−5.44446			−0.509920
$115$	9.33185	−	1.31111i	0.870200	−	0.122261i
$116$	0.592104			0.0549755
$117$		−	13.7096i		−	1.26746i
$118$		−	2.23506i		−	0.205754i
$119$	−0.126900			−0.0116329
$120$	0.214320	+	1.52543i	0.0195646	+	0.139252i
$121$	−10.9541			−0.995824
$122$			11.3620i			1.02866i
$123$			7.31111i			0.659220i
$124$	−3.64296			−0.327147
$125$	−4.54617	−	10.2143i	−0.406622	−	0.913597i
$126$	−4.80642			−0.428190
$127$			6.85728i			0.608485i	0.952595	+	0.304243i	$0.0984033\pi$
$127$			6.85728i			0.608485i	−0.952595	+	0.304243i	$0.901597\pi$
$128$			1.00000i			0.0883883i
$129$	−0.688892			−0.0606536
$130$	−1.68889	−	12.0207i	−0.148126	−	1.05429i
$131$	−5.19850			−0.454195			−0.227097	−	0.973872i	$-0.572924\pi$
$131$	−5.19850			−0.454195			−0.227097	+	0.973872i	$0.572924\pi$
$132$			0.147643i			0.0128507i
$133$		−	15.0415i		−	1.30426i
$134$	−15.6430			−1.35135
$135$	8.42864	−	1.18421i	0.725422	−	0.101920i
$136$	0.0666765			0.00571747
$137$			13.3017i			1.13644i	0.822875	+	0.568222i	$0.192369\pi$
$137$			13.3017i			1.13644i	−0.822875	+	0.568222i	$0.807631\pi$
$138$			2.90321i			0.247138i
$139$	−8.25581			−0.700248			−0.350124	−	0.936703i	$-0.613861\pi$
$139$	−8.25581			−0.700248			−0.350124	+	0.936703i	$0.613861\pi$
$140$	−4.21432	+	0.592104i	−0.356175	+	0.0500419i
$141$	5.23014			0.440457
$142$		−	6.16839i		−	0.517640i
$143$		−	1.16346i		−	0.0972938i
$144$	2.52543			0.210452
$145$	−0.184208	−	1.31111i	−0.0152977	−	0.108882i
$146$	15.2558			1.26258
$147$		−	2.32693i		−	0.191922i
$148$		−	2.02074i		−	0.166104i
$149$	−5.92396			−0.485309			−0.242655	−	0.970113i	$-0.578018\pi$
$149$	−5.92396			−0.485309			−0.242655	+	0.970113i	$0.578018\pi$
$150$	3.31111	−	0.949145i	0.270351	−	0.0774974i
$151$	−15.1842			−1.23567			−0.617837	−	0.786306i	$-0.711991\pi$
$151$	−15.1842			−1.23567			−0.617837	+	0.786306i	$0.711991\pi$
$152$			7.90321i			0.641035i
$153$		−	0.168387i		−	0.0136133i
$154$	−0.407896			−0.0328692
$155$	1.13335	+	8.06668i	0.0910331	+	0.647931i
$156$	3.73975			0.299419
$157$		−	7.75404i		−	0.618840i	−0.950926	−	0.309420i	$-0.899865\pi$
$157$		−	7.75404i		−	0.618840i	0.950926	−	0.309420i	$-0.100135\pi$
$158$		−	2.93332i		−	0.233363i
$159$	5.90813			0.468546
$160$	2.21432	−	0.311108i	0.175057	−	0.0245952i
$161$	−8.02074			−0.632123
$162$		−	4.95407i		−	0.389228i
$163$			11.0509i			0.865570i	0.901497	+	0.432785i	$0.142469\pi$
$163$			11.0509i			0.865570i	−0.901497	+	0.432785i	$0.857531\pi$
$164$	10.6128			0.828724
$165$	0.326929	−	0.0459330i	0.0254514	−	0.00357588i
$166$	8.18913			0.635600
$167$		−	6.50961i		−	0.503728i	−0.967763	−	0.251864i	$-0.918956\pi$
$167$		−	6.50961i		−	0.503728i	0.967763	−	0.251864i	$-0.0810436\pi$
$168$		−	1.31111i		−	0.101154i
$169$	−16.4701			−1.26693
$170$	−0.0207436	−	0.147643i	−0.00159096	−	0.0113237i
$171$	19.9590			1.52630
$172$			1.00000i			0.0762493i
$173$			1.75557i			0.133473i	0.997771	+	0.0667367i	$0.0212588\pi$
$173$			1.75557i			0.133473i	−0.997771	+	0.0667367i	$0.978741\pi$
$174$	0.407896			0.0309225
$175$	2.62222	+	9.14764i	0.198221	+	0.691497i
$176$	0.214320			0.0161550
$177$		−	1.53972i		−	0.115732i
$178$		−	15.9605i		−	1.19629i
$179$	−0.0365650			−0.00273300			−0.00136650	−	0.999999i	$-0.500435\pi$
$179$	−0.0365650			−0.00273300			−0.00136650	+	0.999999i	$0.500435\pi$
$180$	−0.785680	−	5.59210i	−0.0585611	−	0.416811i
$181$	−7.54617			−0.560902			−0.280451	−	0.959868i	$-0.590484\pi$
$181$	−7.54617			−0.560902			−0.280451	+	0.959868i	$0.590484\pi$
$182$			10.3319i			0.765848i
$183$			7.82717i			0.578601i
$184$	4.21432			0.310684
$185$	−4.47457	+	0.628669i	−0.328977	+	0.0462207i
$186$	−2.50961			−0.184013
$187$		−	0.0142901i		−	0.00104500i
$188$		−	7.59210i		−	0.553711i
$189$	−7.24443			−0.526955
$190$	17.5002	−	2.45875i	1.26960	−	0.178377i
$191$	−1.17775			−0.0852193			−0.0426097	−	0.999092i	$-0.513567\pi$
$191$	−1.17775			−0.0852193			−0.0426097	+	0.999092i	$0.513567\pi$
$192$			0.688892i			0.0497165i
$193$			8.23506i			0.592773i	0.955068	+	0.296386i	$0.0957816\pi$
$193$			8.23506i			0.592773i	−0.955068	+	0.296386i	$0.904218\pi$
$194$	2.06668			0.148379
$195$	−1.16346	−	8.28100i	−0.0833174	−	0.593014i
$196$	−3.37778			−0.241270
$197$			0.00492217i			0.000350690i	1.00000		0.000175345i	$5.58141e-5\pi$
$197$			0.00492217i			0.000350690i	−1.00000		0.000175345i	$0.999944\pi$
$198$		−	0.541249i		−	0.0384649i
$199$	22.4035			1.58814			0.794069	−	0.607827i	$-0.207959\pi$
$199$	22.4035			1.58814			0.794069	+	0.607827i	$0.207959\pi$
$200$	−1.37778	−	4.80642i	−0.0974241	−	0.339865i
$201$	−10.7763			−0.760102
$202$			7.60639i			0.535184i
$203$			1.12690i			0.0790928i
$204$	0.0459330			0.00321595
$205$	−3.30174	−	23.5002i	−0.230604	−	1.64133i
$206$	−5.18421			−0.361201
$207$		−	10.6430i		−	0.739737i
$208$		−	5.42864i		−	0.376408i
$209$	1.69381			0.117164
$210$	−2.90321	+	0.407896i	−0.200341	+	0.0281475i
$211$	−21.3274			−1.46824			−0.734120	−	0.679020i	$-0.762405\pi$
$211$	−21.3274			−1.46824			−0.734120	+	0.679020i	$0.762405\pi$
$212$		−	8.57628i		−	0.589022i
$213$		−	4.24935i		−	0.291161i
$214$	16.9748			1.16037
$215$	2.21432	−	0.311108i	0.151015	−	0.0212174i
$216$	3.80642			0.258994
$217$		−	6.93332i		−	0.470665i
$218$			9.47949i			0.642032i
$219$	10.5096			0.710173
$220$	−0.0666765	−	0.474572i	−0.00449533	−	0.0319957i
$221$	−0.361963			−0.0243483
$222$		−	1.39207i		−	0.0934299i
$223$		−	15.9541i		−	1.06836i	−0.845370	−	0.534182i	$-0.820620\pi$
$223$		−	15.9541i		−	1.06836i	0.845370	−	0.534182i	$-0.179380\pi$
$224$	−1.90321			−0.127164
$225$	−12.1383	+	3.47949i	−0.809218	+	0.231966i
$226$	−1.82225			−0.121214
$227$		−	15.7462i		−	1.04511i	−0.852605	−	0.522556i	$-0.824979\pi$
$227$		−	15.7462i		−	1.04511i	0.852605	−	0.522556i	$-0.175021\pi$
$228$			5.44446i			0.360568i
$229$	1.00937			0.0667009			0.0333505	−	0.999444i	$-0.489382\pi$
$229$	1.00937			0.0667009			0.0333505	+	0.999444i	$0.489382\pi$
$230$	−1.31111	−	9.33185i	−0.0864519	−	0.615324i
$231$	−0.280996			−0.0184882
$232$		−	0.592104i		−	0.0388735i
$233$			5.29036i			0.346583i	0.984871	+	0.173292i	$0.0554403\pi$
$233$			5.29036i			0.346583i	−0.984871	+	0.173292i	$0.944560\pi$
$234$	−13.7096			−0.896227
$235$	−16.8113	+	2.36196i	−1.09665	+	0.154077i
$236$	−2.23506			−0.145490
$237$		−	2.02074i		−	0.131261i
$238$			0.126900i			0.00822568i
$239$	−8.02567			−0.519137			−0.259569	−	0.965725i	$-0.583580\pi$
$239$	−8.02567			−0.519137			−0.259569	+	0.965725i	$0.583580\pi$
$240$	1.52543	−	0.214320i	0.0984659	−	0.0138343i
$241$	15.3067			0.985989			0.492994	−	0.870032i	$-0.335902\pi$
$241$	15.3067			0.985989			0.492994	+	0.870032i	$0.335902\pi$
$242$			10.9541i			0.704154i
$243$		−	14.8321i		−	0.951479i
$244$	11.3620			0.727375
$245$	1.05086	+	7.47949i	0.0671367	+	0.477847i
$246$	7.31111			0.466139
$247$		−	42.9037i		−	2.72990i
$248$			3.64296i			0.231328i
$249$	5.64143			0.357511
$250$	−10.2143	+	4.54617i	−0.646010	+	0.287525i
$251$	26.3783			1.66498			0.832491	−	0.554039i	$-0.186914\pi$
$251$	26.3783			1.66498			0.832491	+	0.554039i	$0.186914\pi$
$252$			4.80642i			0.302776i
$253$		−	0.903212i		−	0.0567844i
$254$	6.85728			0.430264
$255$	−0.0142901	−	0.101710i	−0.000894881	−	0.00636934i
$256$	1.00000			0.0625000
$257$		−	17.5368i		−	1.09392i	−0.837160	−	0.546958i	$-0.815786\pi$
$257$		−	17.5368i		−	1.09392i	0.837160	−	0.546958i	$-0.184214\pi$
$258$			0.688892i			0.0428886i
$259$	3.84590			0.238973
$260$	−12.0207	+	1.68889i	−0.745495	+	0.104741i
$261$	−1.49532			−0.0925577
$262$			5.19850i			0.321164i
$263$			0.644491i			0.0397410i	0.999803	+	0.0198705i	$0.00632539\pi$
$263$			0.644491i			0.0397410i	−0.999803	+	0.0198705i	$0.993675\pi$
$264$	0.147643			0.00908681
$265$	−18.9906	+	2.66815i	−1.16659	+	0.163903i
$266$	−15.0415			−0.922253
$267$		−	10.9951i		−	0.672888i
$268$			15.6430i			0.955546i
$269$	−26.8256			−1.63559			−0.817794	−	0.575511i	$-0.804803\pi$
$269$	−26.8256			−1.63559			−0.817794	+	0.575511i	$0.804803\pi$
$270$	−1.18421	−	8.42864i	−0.0720686	−	0.512951i
$271$	−25.5827			−1.55404			−0.777020	−	0.629476i	$-0.783270\pi$
$271$	−25.5827			−1.55404			−0.777020	+	0.629476i	$0.783270\pi$
$272$		−	0.0666765i		−	0.00404286i
$273$			7.11753i			0.430773i
$274$	13.3017			0.803587
$275$	−1.03011	+	0.295286i	−0.0621181	+	0.0178064i
$276$	2.90321			0.174753
$277$		−	11.2444i		−	0.675612i	−0.941216	−	0.337806i	$-0.890315\pi$
$277$		−	11.2444i		−	0.675612i	0.941216	−	0.337806i	$-0.109685\pi$
$278$			8.25581i			0.495150i
$279$	9.20003			0.550791
$280$	0.592104	+	4.21432i	0.0353850	+	0.251854i
$281$	20.7462			1.23761			0.618807	−	0.785543i	$-0.287616\pi$
$281$	20.7462			1.23761			0.618807	+	0.785543i	$0.287616\pi$
$282$		−	5.23014i		−	0.311450i
$283$			3.82225i			0.227209i	0.993526	+	0.113604i	$0.0362397\pi$
$283$			3.82225i			0.227209i	−0.993526	+	0.113604i	$0.963760\pi$
$284$	−6.16839			−0.366026
$285$	12.0558	−	1.69381i	0.714123	−	0.100333i
$286$	−1.16346			−0.0687971
$287$			20.1985i			1.19228i
$288$		−	2.52543i		−	0.148812i
$289$	16.9956			0.999738
$290$	−1.31111	+	0.184208i	−0.0769909	+	0.0108171i
$291$	1.42372			0.0834598
$292$		−	15.2558i		−	0.892779i
$293$			23.9398i			1.39858i	0.714840	+	0.699288i	$0.246500\pi$
$293$			23.9398i			1.39858i	−0.714840	+	0.699288i	$0.753500\pi$
$294$	−2.32693			−0.135709
$295$	0.695346	+	4.94914i	0.0404846	+	0.288150i
$296$	−2.02074			−0.117453
$297$		−	0.815792i		−	0.0473370i
$298$			5.92396i			0.343166i
$299$	−22.8780			−1.32307
$300$	−0.949145	−	3.31111i	−0.0547989	−	0.191167i
$301$	−1.90321			−0.109699
$302$			15.1842i			0.873753i
$303$			5.23999i			0.301029i
$304$	7.90321			0.453280
$305$	−3.53480	−	25.1590i	−0.202402	−	1.44060i
$306$	−0.168387			−0.00962603
$307$			10.3713i			0.591923i	0.955200	+	0.295962i	$0.0956400\pi$
$307$			10.3713i			0.591923i	−0.955200	+	0.295962i	$0.904360\pi$
$308$			0.407896i			0.0232420i
$309$	−3.57136			−0.203168
$310$	8.06668	−	1.13335i	0.458156	−	0.0643701i
$311$	23.9240			1.35660			0.678302	−	0.734784i	$-0.262716\pi$
$311$	23.9240			1.35660			0.678302	+	0.734784i	$0.262716\pi$
$312$		−	3.73975i		−	0.211721i
$313$			2.94914i			0.166696i	0.996521	+	0.0833478i	$0.0265612\pi$
$313$			2.94914i			0.166696i	−0.996521	+	0.0833478i	$0.973439\pi$
$314$	−7.75404			−0.437586
$315$	10.6430	−	1.49532i	0.599663	−	0.0842515i
$316$	−2.93332			−0.165012
$317$		−	8.76049i		−	0.492038i	−0.969265	−	0.246019i	$-0.920877\pi$
$317$		−	8.76049i		−	0.492038i	0.969265	−	0.246019i	$-0.0791226\pi$
$318$		−	5.90813i		−	0.331312i
$319$	−0.126900			−0.00710501
$320$	−0.311108	−	2.21432i	−0.0173915	−	0.123784i
$321$	11.6938			0.652685
$322$			8.02074i			0.446979i
$323$		−	0.526959i		−	0.0293208i
$324$	−4.95407			−0.275226
$325$	7.47949	+	26.0923i	0.414888	+	1.44734i
$326$	11.0509			0.612050
$327$			6.53035i			0.361129i
$328$		−	10.6128i		−	0.585996i
$329$	14.4494			0.796620
$330$	−0.0459330	−	0.326929i	−0.00252853	−	0.0179969i
$331$	14.1476			0.777625			0.388812	−	0.921317i	$-0.372885\pi$
$331$	14.1476			0.777625			0.388812	+	0.921317i	$0.372885\pi$
$332$		−	8.18913i		−	0.449437i
$333$			5.10324i			0.279656i
$334$	−6.50961			−0.356190
$335$	34.6385	−	4.86665i	1.89250	−	0.265893i
$336$	−1.31111			−0.0715268
$337$			24.2034i			1.31844i	0.751948	+	0.659222i	$0.229114\pi$
$337$			24.2034i			1.31844i	−0.751948	+	0.659222i	$0.770886\pi$
$338$			16.4701i			0.895857i
$339$	−1.25533			−0.0681802
$340$	−0.147643	+	0.0207436i	−0.00800708	+	0.00112498i
$341$	0.780758			0.0422804
$342$		−	19.9590i		−	1.07926i
$343$		−	19.7511i		−	1.06646i
$344$	1.00000			0.0539164
$345$	−0.903212	−	6.42864i	−0.0486273	−	0.346106i
$346$	1.75557			0.0943800
$347$			28.3116i			1.51985i	0.650013	+	0.759923i	$0.274763\pi$
$347$			28.3116i			1.51985i	−0.650013	+	0.759923i	$0.725237\pi$
$348$		−	0.407896i		−	0.0218655i
$349$	13.1842			0.705734			0.352867	−	0.935673i	$-0.385207\pi$
$349$	13.1842			0.705734			0.352867	+	0.935673i	$0.385207\pi$
$350$	9.14764	−	2.62222i	0.488962	−	0.140163i
$351$	−20.6637			−1.10295
$352$		−	0.214320i		−	0.0114233i
$353$			29.3812i			1.56380i	0.623403	+	0.781901i	$0.285750\pi$
$353$			29.3812i			1.56380i	−0.623403	+	0.781901i	$0.714250\pi$
$354$	−1.53972			−0.0818351
$355$	1.91903	+	13.6588i	0.101852	+	0.724933i
$356$	−15.9605			−0.845906
$357$			0.0874201i			0.00462676i
$358$			0.0365650i			0.00193252i
$359$	−26.6795			−1.40809			−0.704046	−	0.710155i	$-0.748625\pi$
$359$	−26.6795			−1.40809			−0.704046	+	0.710155i	$0.748625\pi$
$360$	−5.59210	+	0.785680i	−0.294730	+	0.0414090i
$361$	43.4608			2.28741
$362$			7.54617i			0.396618i
$363$			7.54617i			0.396071i
$364$	10.3319			0.541536
$365$	−33.7812	+	4.74620i	−1.76819	+	0.248428i
$366$	7.82717			0.409133
$367$			27.1941i			1.41952i	0.704445	+	0.709759i	$0.251196\pi$
$367$			27.1941i			1.41952i	−0.704445	+	0.709759i	$0.748804\pi$
$368$		−	4.21432i		−	0.219687i
$369$	−26.8020			−1.39526
$370$	0.628669	+	4.47457i	0.0326830	+	0.232622i
$371$	16.3225			0.847421
$372$			2.50961i			0.130117i
$373$			0.214320i			0.0110971i	0.999985	+	0.00554853i	$0.00176616\pi$
$373$			0.214320i			0.0110971i	−0.999985	+	0.00554853i	$0.998234\pi$
$374$	−0.0142901			−0.000738924
$375$	−7.03657	+	3.13182i	−0.363367	+	0.161727i
$376$	−7.59210			−0.391533
$377$			3.21432i			0.165546i
$378$			7.24443i			0.372613i
$379$	−3.73329			−0.191766			−0.0958832	−	0.995393i	$-0.530568\pi$
$379$	−3.73329			−0.191766			−0.0958832	+	0.995393i	$0.530568\pi$
$380$	−2.45875	−	17.5002i	−0.126131	−	0.897743i
$381$	4.72393			0.242014
$382$			1.17775i			0.0602592i
$383$		−	15.6035i		−	0.797301i	−0.917103	−	0.398650i	$-0.869479\pi$
$383$		−	15.6035i		−	0.797301i	0.917103	−	0.398650i	$-0.130521\pi$
$384$	0.688892			0.0351549
$385$	0.903212	−	0.126900i	0.0460319	−	0.00646740i
$386$	8.23506			0.419154
$387$		−	2.52543i		−	0.128375i
$388$		−	2.06668i		−	0.104920i
$389$	−36.1847			−1.83464			−0.917318	−	0.398155i	$-0.869651\pi$
$389$	−36.1847			−1.83464			−0.917318	+	0.398155i	$0.869651\pi$
$390$	−8.28100	+	1.16346i	−0.419325	+	0.0589143i
$391$	−0.280996			−0.0142106
$392$			3.37778i			0.170604i
$393$			3.58120i			0.180648i
$394$	0.00492217			0.000247975
$395$	0.912580	+	6.49532i	0.0459169	+	0.326815i
$396$	−0.541249			−0.0271988
$397$		−	18.9032i		−	0.948725i	−0.880330	−	0.474363i	$-0.842679\pi$
$397$		−	18.9032i		−	0.948725i	0.880330	−	0.474363i	$-0.157321\pi$
$398$		−	22.4035i		−	1.12298i
$399$	−10.3620			−0.518747
$400$	−4.80642	+	1.37778i	−0.240321	+	0.0688892i
$401$	−23.0098			−1.14906			−0.574528	−	0.818485i	$-0.694815\pi$
$401$	−23.0098			−1.14906			−0.574528	+	0.818485i	$0.694815\pi$
$402$			10.7763i			0.537474i
$403$		−	19.7763i		−	0.985128i
$404$	7.60639			0.378432
$405$	1.54125	+	10.9699i	0.0765853	+	0.545098i
$406$	1.12690			0.0559271
$407$			0.433085i			0.0214672i
$408$		−	0.0459330i		−	0.00227402i
$409$	21.3669			1.05652			0.528262	−	0.849081i	$-0.322844\pi$
$409$	21.3669			1.05652			0.528262	+	0.849081i	$0.322844\pi$
$410$	−23.5002	+	3.30174i	−1.16059	+	0.163061i
$411$	9.16346			0.452000
$412$			5.18421i			0.255408i
$413$		−	4.25380i		−	0.209316i
$414$	−10.6430			−0.523073
$415$	−18.1334	+	2.54770i	−0.890131	+	0.125062i
$416$	−5.42864			−0.266161
$417$			5.68736i			0.278511i
$418$		−	1.69381i		−	0.0828472i
$419$	11.6365			0.568481			0.284240	−	0.958753i	$-0.408259\pi$
$419$	11.6365			0.568481			0.284240	+	0.958753i	$0.408259\pi$
$420$	0.407896	+	2.90321i	0.0199033	+	0.141662i
$421$	24.3798			1.18820			0.594099	−	0.804392i	$-0.297509\pi$
$421$	24.3798			1.18820			0.594099	+	0.804392i	$0.297509\pi$
$422$			21.3274i			1.03820i
$423$			19.1733i			0.932238i
$424$	−8.57628			−0.416501
$425$	0.0918659	+	0.320476i	0.00445615	+	0.0155454i
$426$	−4.24935			−0.205882
$427$			21.6242i			1.04647i
$428$		−	16.9748i		−	0.820508i
$429$	−0.801502			−0.0386969
$430$	−0.311108	−	2.21432i	−0.0150030	−	0.106784i
$431$	−21.4050			−1.03104			−0.515521	−	0.856877i	$-0.672402\pi$
$431$	−21.4050			−1.03104			−0.515521	+	0.856877i	$0.672402\pi$
$432$		−	3.80642i		−	0.183137i
$433$			19.8464i			0.953756i	0.878969	+	0.476878i	$0.158232\pi$
$433$			19.8464i			0.953756i	−0.878969	+	0.476878i	$0.841768\pi$
$434$	−6.93332			−0.332810
$435$	−0.903212	+	0.126900i	−0.0433057	+	0.00608437i
$436$	9.47949			0.453985
$437$		−	33.3067i		−	1.59327i
$438$		−	10.5096i		−	0.502168i
$439$	34.5433			1.64866			0.824330	−	0.566110i	$-0.191552\pi$
$439$	34.5433			1.64866			0.824330	+	0.566110i	$0.191552\pi$
$440$	−0.474572	+	0.0666765i	−0.0226244	+	0.00317868i
$441$	8.53035			0.406207
$442$			0.361963i			0.0172168i
$443$		−	0.698260i		−	0.0331753i	−0.999862	−	0.0165877i	$-0.994720\pi$
$443$		−	0.698260i		−	0.0331753i	0.999862	−	0.0165877i	$-0.00528026\pi$
$444$	−1.39207			−0.0660649
$445$	4.96544	+	35.3417i	0.235385	+	1.67536i
$446$	−15.9541			−0.755447
$447$			4.08097i			0.193023i
$448$			1.90321i			0.0899183i
$449$	13.7955			0.651051			0.325526	−	0.945533i	$-0.394459\pi$
$449$	13.7955			0.651051			0.325526	+	0.945533i	$0.394459\pi$
$450$	3.47949	+	12.1383i	0.164025	+	0.572204i
$451$	−2.27454			−0.107104
$452$			1.82225i			0.0857112i
$453$			10.4603i			0.491467i
$454$	−15.7462			−0.739006
$455$	−3.21432	−	22.8780i	−0.150690	−	1.07254i
$456$	5.44446			0.254960
$457$		−	27.9813i		−	1.30891i	−0.756102	−	0.654454i	$-0.772898\pi$
$457$		−	27.9813i		−	1.30891i	0.756102	−	0.654454i	$-0.227102\pi$
$458$		−	1.00937i		−	0.0471647i
$459$	−0.253799			−0.0118463
$460$	−9.33185	+	1.31111i	−0.435100	+	0.0611307i
$461$	40.6671			1.89406			0.947028	−	0.321152i	$-0.104070\pi$
$461$	40.6671			1.89406			0.947028	+	0.321152i	$0.104070\pi$
$462$			0.280996i			0.0130731i
$463$			3.87463i			0.180069i	0.995939	+	0.0900347i	$0.0286978\pi$
$463$			3.87463i			0.180069i	−0.995939	+	0.0900347i	$0.971302\pi$
$464$	−0.592104			−0.0274877
$465$	5.55707	−	0.780758i	0.257703	−	0.0362068i
$466$	5.29036			0.245071
$467$		−	6.62867i		−	0.306738i	−0.988169	−	0.153369i	$-0.950988\pi$
$467$		−	6.62867i		−	0.306738i	0.988169	−	0.153369i	$-0.0490123\pi$
$468$			13.7096i			0.633728i
$469$	−29.7719			−1.37474
$470$	2.36196	+	16.8113i	0.108949	+	0.775450i
$471$	−5.34170			−0.246132
$472$			2.23506i			0.102877i
$473$		−	0.214320i		−	0.00985443i
$474$	−2.02074			−0.0928158
$475$	−37.9862	+	10.8889i	−1.74293	+	0.499618i
$476$	0.126900			0.00581643
$477$			21.6588i			0.991687i
$478$			8.02567i			0.367085i
$479$	25.8894			1.18292			0.591458	−	0.806336i	$-0.298552\pi$
$479$	25.8894			1.18292			0.591458	+	0.806336i	$0.298552\pi$
$480$	−0.214320	−	1.52543i	−0.00978231	−	0.0696259i
$481$	10.9699			0.500184
$482$		−	15.3067i		−	0.697199i
$483$			5.52543i			0.251416i
$484$	10.9541			0.497912
$485$	−4.57628	+	0.642959i	−0.207798	+	0.0291953i
$486$	−14.8321			−0.672797
$487$			9.43017i			0.427322i	0.976908	+	0.213661i	$0.0685388\pi$
$487$			9.43017i			0.427322i	−0.976908	+	0.213661i	$0.931461\pi$
$488$		−	11.3620i		−	0.514332i
$489$	7.61285			0.344265
$490$	7.47949	−	1.05086i	0.337889	−	0.0474728i
$491$	−2.14764			−0.0969218			−0.0484609	−	0.998825i	$-0.515432\pi$
$491$	−2.14764			−0.0969218			−0.0484609	+	0.998825i	$0.515432\pi$
$492$		−	7.31111i		−	0.329610i
$493$			0.0394795i			0.00177807i
$494$	−42.9037			−1.93033
$495$	0.168387	+	1.19850i	0.00756842	+	0.0538685i
$496$	3.64296			0.163574
$497$		−	11.7397i		−	0.526600i
$498$		−	5.64143i		−	0.252798i
$499$	−9.04593			−0.404952			−0.202476	−	0.979287i	$-0.564899\pi$
$499$	−9.04593			−0.404952			−0.202476	+	0.979287i	$0.564899\pi$
$500$	4.54617	+	10.2143i	0.203311	+	0.456798i
$501$	−4.48442			−0.200349
$502$		−	26.3783i		−	1.17732i
$503$		−	39.8751i		−	1.77794i	−0.457962	−	0.888972i	$-0.651421\pi$
$503$		−	39.8751i		−	1.77794i	0.457962	−	0.888972i	$-0.348579\pi$
$504$	4.80642			0.214095
$505$	−2.36641	−	16.8430i	−0.105304	−	0.749503i
$506$	−0.903212			−0.0401527
$507$			11.3461i			0.503900i
$508$		−	6.85728i		−	0.304243i
$509$	7.93978			0.351924			0.175962	−	0.984397i	$-0.443696\pi$
$509$	7.93978			0.351924			0.175962	+	0.984397i	$0.443696\pi$
$510$	−0.101710	+	0.0142901i	−0.00450381	+	0.000632776i
$511$	29.0350			1.28443
$512$		−	1.00000i		−	0.0441942i
$513$		−	30.0830i		−	1.32820i
$514$	−17.5368			−0.773515
$515$	11.4795	−	1.61285i	0.505847	−	0.0710706i
$516$	0.688892			0.0303268
$517$			1.62714i			0.0715614i
$518$		−	3.84590i		−	0.168979i
$519$	1.20940			0.0530867
$520$	1.68889	+	12.0207i	0.0740628	+	0.527144i
$521$	11.7255			0.513702			0.256851	−	0.966451i	$-0.417315\pi$
$521$	11.7255			0.513702			0.256851	+	0.966451i	$0.417315\pi$
$522$			1.49532i			0.0654482i
$523$		−	20.4222i		−	0.893000i	−0.894784	−	0.446500i	$-0.852670\pi$
$523$		−	20.4222i		−	0.893000i	0.894784	−	0.446500i	$-0.147330\pi$
$524$	5.19850			0.227097
$525$	6.30174	−	1.80642i	0.275030	−	0.0788388i
$526$	0.644491			0.0281011
$527$		−	0.242900i		−	0.0105809i
$528$		−	0.147643i		−	0.00642535i
$529$	5.23951			0.227805
$530$	2.66815	+	18.9906i	0.115897	+	0.824900i
$531$	5.64449			0.244950
$532$			15.0415i			0.652131i
$533$			57.6133i			2.49551i
$534$	−10.9951			−0.475804
$535$	−37.5877	+	5.28100i	−1.62506	+	0.228317i
$536$	15.6430			0.675673
$537$			0.0251894i			0.00108700i
$538$			26.8256i			1.15654i
$539$	0.723926			0.0311817
$540$	−8.42864	+	1.18421i	−0.362711	+	0.0509602i
$541$	−34.7338			−1.49332			−0.746661	−	0.665205i	$-0.768344\pi$
$541$	−34.7338			−1.49332			−0.746661	+	0.665205i	$0.768344\pi$
$542$			25.5827i			1.09887i
$543$			5.19850i			0.223089i
$544$	−0.0666765			−0.00285873
$545$	−2.94914	−	20.9906i	−0.126327	−	0.899140i
$546$	7.11753			0.304602
$547$			20.4286i			0.873466i	0.899591	+	0.436733i	$0.143864\pi$
$547$			20.4286i			0.873466i	−0.899591	+	0.436733i	$0.856136\pi$
$548$		−	13.3017i		−	0.568222i
$549$	−28.6938			−1.22462
$550$	0.295286	+	1.03011i	0.0125911	+	0.0439241i
$551$	−4.67952			−0.199354
$552$		−	2.90321i		−	0.123569i
$553$		−	5.58274i		−	0.237402i
$554$	−11.2444			−0.477730
$555$	0.433085	+	3.08250i	0.0183834	+	0.130845i
$556$	8.25581			0.350124
$557$			15.2163i			0.644736i	0.946614	+	0.322368i	$0.104479\pi$
$557$			15.2163i			0.644736i	−0.946614	+	0.322368i	$0.895521\pi$
$558$		−	9.20003i		−	0.389468i
$559$	−5.42864			−0.229607
$560$	4.21432	−	0.592104i	0.178088	−	0.0250210i
$561$	−0.00984434			−0.000415628
$562$		−	20.7462i		−	0.875126i
$563$		−	10.3254i		−	0.435164i	−0.976042	−	0.217582i	$-0.930183\pi$
$563$		−	10.3254i		−	0.435164i	0.976042	−	0.217582i	$-0.0698169\pi$
$564$	−5.23014			−0.220229
$565$	4.03503	−	0.566915i	0.169755	−	0.0238503i
$566$	3.82225			0.160661
$567$		−	9.42864i		−	0.395966i
$568$			6.16839i			0.258820i
$569$	0.668625			0.0280302			0.0140151	−	0.999902i	$-0.495539\pi$
$569$	0.668625			0.0280302			0.0140151	+	0.999902i	$0.495539\pi$
$570$	−1.69381	−	12.0558i	−0.0709461	−	0.504961i
$571$	−26.4005			−1.10483			−0.552414	−	0.833570i	$-0.686293\pi$
$571$	−26.4005			−1.10483			−0.552414	+	0.833570i	$0.686293\pi$
$572$			1.16346i			0.0486469i
$573$			0.811346i			0.0338945i
$574$	20.1985			0.843069
$575$	5.80642	+	20.2558i	0.242145	+	0.844726i
$576$	−2.52543			−0.105226
$577$			21.7032i			0.903515i	0.892141	+	0.451758i	$0.149203\pi$
$577$			21.7032i			0.903515i	−0.892141	+	0.451758i	$0.850797\pi$
$578$		−	16.9956i		−	0.706922i
$579$	5.67307			0.235765
$580$	0.184208	+	1.31111i	0.00764883	+	0.0544408i
$581$	15.5857			0.646602
$582$		−	1.42372i		−	0.0590150i
$583$			1.83807i			0.0761249i
$584$	−15.2558			−0.631290
$585$	30.3575	−	4.26517i	1.25513	−	0.176343i
$586$	23.9398			0.988943
$587$		−	4.44494i		−	0.183462i	−0.995784	−	0.0917311i	$-0.970760\pi$
$587$		−	4.44494i		−	0.183462i	0.995784	−	0.0917311i	$-0.0292400\pi$
$588$			2.32693i			0.0959609i
$589$	28.7911			1.18632
$590$	4.94914	−	0.695346i	0.203753	−	0.0286269i
$591$	0.00339084			0.000139481
$592$			2.02074i			0.0830521i
$593$		−	41.8691i		−	1.71936i	−0.510834	−	0.859680i	$-0.670663\pi$
$593$		−	41.8691i		−	1.71936i	0.510834	−	0.859680i	$-0.329337\pi$
$594$	−0.815792			−0.0334723
$595$	−0.0394795	−	0.280996i	−0.00161850	−	0.0115197i
$596$	5.92396			0.242655
$597$		−	15.4336i		−	0.631654i
$598$			22.8780i			0.935552i
$599$	−28.7654			−1.17532			−0.587661	−	0.809107i	$-0.699951\pi$
$599$	−28.7654			−1.17532			−0.587661	+	0.809107i	$0.699951\pi$
$600$	−3.31111	+	0.949145i	−0.135175	+	0.0387487i
$601$	35.1624			1.43430			0.717152	−	0.696916i	$-0.245445\pi$
$601$	35.1624			1.43430			0.717152	+	0.696916i	$0.245445\pi$
$602$			1.90321i			0.0775691i
$603$		−	39.5052i		−	1.60877i
$604$	15.1842			0.617837
$605$	−3.40790	−	24.2558i	−0.138551	−	0.986139i
$606$	5.23999			0.212860
$607$		−	32.5990i		−	1.32315i	−0.749877	−	0.661577i	$-0.769887\pi$
$607$		−	32.5990i		−	1.32315i	0.749877	−	0.661577i	$-0.230113\pi$
$608$		−	7.90321i		−	0.320518i
$609$	0.776312			0.0314578
$610$	−25.1590	+	3.53480i	−1.01866	+	0.143120i
$611$	41.2148			1.66737
$612$			0.168387i			0.00680663i
$613$		−	2.46965i		−	0.0997482i	−0.998756	−	0.0498741i	$-0.984118\pi$
$613$		−	2.46965i		−	0.0997482i	0.998756	−	0.0498741i	$-0.0158820\pi$
$614$	10.3713			0.418553
$615$	−16.1891	+	2.27454i	−0.652809	+	0.0917184i
$616$	0.407896			0.0164346
$617$		−	21.9081i		−	0.881988i	−0.897510	−	0.440994i	$-0.854626\pi$
$617$		−	21.9081i		−	0.881988i	0.897510	−	0.440994i	$-0.145374\pi$
$618$			3.57136i			0.143661i
$619$	−27.6751			−1.11236			−0.556178	−	0.831063i	$-0.687733\pi$
$619$	−27.6751			−1.11236			−0.556178	+	0.831063i	$0.687733\pi$
$620$	−1.13335	−	8.06668i	−0.0455166	−	0.323966i
$621$	−16.0415			−0.643723
$622$		−	23.9240i		−	0.959263i
$623$		−	30.3763i		−	1.21700i
$624$	−3.73975			−0.149710
$625$	21.2034	−	13.2444i	0.848137	−	0.529777i
$626$	2.94914			0.117872
$627$		−	1.16686i		−	0.0465997i
$628$			7.75404i			0.309420i
$629$	0.134736			0.00537228
$630$	−1.49532	−	10.6430i	−0.0595748	−	0.424026i
$631$	31.5591			1.25635			0.628174	−	0.778073i	$-0.283803\pi$
$631$	31.5591			1.25635			0.628174	+	0.778073i	$0.283803\pi$
$632$			2.93332i			0.116681i
$633$			14.6923i			0.583966i
$634$	−8.76049			−0.347924
$635$	−15.1842	+	2.13335i	−0.602567	+	0.0846595i
$636$	−5.90813			−0.234273
$637$		−	18.3368i		−	0.726529i
$638$			0.126900i			0.00502400i
$639$	15.5778			0.616249
$640$	−2.21432	+	0.311108i	−0.0875287	+	0.0122976i
$641$	6.78415			0.267958			0.133979	−	0.990984i	$-0.457225\pi$
$641$	6.78415			0.267958			0.133979	+	0.990984i	$0.457225\pi$
$642$		−	11.6938i		−	0.461518i
$643$		−	22.5047i		−	0.887498i	−0.896151	−	0.443749i	$-0.853648\pi$
$643$		−	22.5047i		−	0.887498i	0.896151	−	0.443749i	$-0.146352\pi$
$644$	8.02074			0.316062
$645$	−0.214320	−	1.52543i	−0.00843883	−	0.0600637i
$646$	−0.526959			−0.0207329
$647$			32.3176i			1.27053i	0.772292	+	0.635267i	$0.219110\pi$
$647$			32.3176i			1.27053i	−0.772292	+	0.635267i	$0.780890\pi$
$648$			4.95407i			0.194614i
$649$	0.479018			0.0188031
$650$	26.0923	−	7.47949i	1.02343	−	0.293370i
$651$	−4.77631			−0.187198
$652$		−	11.0509i		−	0.432785i
$653$			16.1728i			0.632892i	0.948611	+	0.316446i	$0.102490\pi$
$653$			16.1728i			0.632892i	−0.948611	+	0.316446i	$0.897510\pi$
$654$	6.53035			0.255357
$655$	−1.61729	−	11.5111i	−0.0631929	−	0.449777i
$656$	−10.6128			−0.414362
$657$			38.5274i			1.50310i
$658$		−	14.4494i		−	0.563296i
$659$	−21.5319			−0.838763			−0.419382	−	0.907810i	$-0.637753\pi$
$659$	−21.5319			−0.838763			−0.419382	+	0.907810i	$0.637753\pi$
$660$	−0.326929	+	0.0459330i	−0.0127257	+	0.00178794i
$661$	−26.8637			−1.04488			−0.522439	−	0.852677i	$-0.674978\pi$
$661$	−26.8637			−1.04488			−0.522439	+	0.852677i	$0.674978\pi$
$662$		−	14.1476i		−	0.549864i
$663$			0.249353i			0.00968409i
$664$	−8.18913			−0.317800
$665$	33.3067	−	4.67952i	1.29158	−	0.181464i
$666$	5.10324			0.197747
$667$			2.49532i			0.0966190i
$668$			6.50961i			0.251864i
$669$	−10.9906			−0.424922
$670$	−4.86665	−	34.6385i	−0.188015	−	1.33820i
$671$	−2.43509			−0.0940057
$672$			1.31111i			0.0505771i
$673$			2.38562i			0.0919589i	0.998942	+	0.0459795i	$0.0146409\pi$
$673$			2.38562i			0.0919589i	−0.998942	+	0.0459795i	$0.985359\pi$
$674$	24.2034			0.932281
$675$	5.24443	+	18.2953i	0.201858	+	0.704186i
$676$	16.4701			0.633466
$677$			27.7877i			1.06797i	0.845495	+	0.533984i	$0.179306\pi$
$677$			27.7877i			1.06797i	−0.845495	+	0.533984i	$0.820694\pi$
$678$			1.25533i			0.0482107i
$679$	3.93332			0.150947
$680$	0.0207436	+	0.147643i	0.000795481	+	0.00566186i
$681$	−10.8474			−0.415675
$682$		−	0.780758i		−	0.0298968i
$683$		−	33.2444i		−	1.27206i	−0.771663	−	0.636031i	$-0.780575\pi$
$683$		−	33.2444i		−	1.27206i	0.771663	−	0.636031i	$-0.219425\pi$
$684$	−19.9590			−0.763151
$685$	−29.4543	+	4.13828i	−1.12539	+	0.158115i
$686$	−19.7511			−0.754101
$687$		−	0.695346i		−	0.0265291i
$688$		−	1.00000i		−	0.0381246i
$689$	46.5575			1.77370
$690$	−6.42864	+	0.903212i	−0.244734	+	0.0343847i
$691$	−24.9951			−0.950858			−0.475429	−	0.879754i	$-0.657707\pi$
$691$	−24.9951			−0.950858			−0.475429	+	0.879754i	$0.657707\pi$
$692$		−	1.75557i		−	0.0667367i
$693$		−	1.03011i		−	0.0391307i
$694$	28.3116			1.07469
$695$	−2.56845	−	18.2810i	−0.0974267	−	0.693438i
$696$	−0.407896			−0.0154613
$697$			0.707628i			0.0268033i
$698$		−	13.1842i		−	0.499030i
$699$	3.64449			0.137847
$700$	−2.62222	−	9.14764i	−0.0991104	−	0.345748i
$701$	−22.0065			−0.831172			−0.415586	−	0.909554i	$-0.636424\pi$
$701$	−22.0065			−0.831172			−0.415586	+	0.909554i	$0.636424\pi$
$702$			20.6637i			0.779901i
$703$			15.9704i			0.602334i
$704$	−0.214320			−0.00807748
$705$	1.62714	+	11.5812i	0.0612816	+	0.436173i
$706$	29.3812			1.10578
$707$			14.4766i			0.544448i
$708$			1.53972i			0.0578661i
$709$	−10.2099			−0.383440			−0.191720	−	0.981450i	$-0.561407\pi$
$709$	−10.2099			−0.383440			−0.191720	+	0.981450i	$0.561407\pi$
$710$	13.6588	−	1.91903i	0.512605	−	0.0720200i
$711$	7.40790			0.277818
$712$			15.9605i			0.598146i
$713$		−	15.3526i		−	0.574959i
$714$	0.0874201			0.00327162
$715$	2.57628	−	0.361963i	0.0963475	−	0.0135366i
$716$	0.0365650			0.00136650
$717$			5.52882i			0.206478i
$718$			26.6795i			0.995671i
$719$	21.5165			0.802431			0.401216	−	0.915984i	$-0.368588\pi$
$719$	21.5165			0.802431			0.401216	+	0.915984i	$0.368588\pi$
$720$	0.785680	+	5.59210i	0.0292806	+	0.208405i
$721$	−9.86665			−0.367453
$722$		−	43.4608i		−	1.61744i
$723$		−	10.5446i		−	0.392159i
$724$	7.54617			0.280451
$725$	2.84590	−	0.815792i	0.105694	−	0.0302977i
$726$	7.54617			0.280065
$727$		−	27.5955i		−	1.02346i	−0.859146	−	0.511730i	$-0.829005\pi$
$727$		−	27.5955i		−	1.02346i	0.859146	−	0.511730i	$-0.170995\pi$
$728$		−	10.3319i		−	0.382924i
$729$	4.64449			0.172018
$730$	4.74620	+	33.7812i	0.175665	+	1.25030i
$731$	−0.0666765			−0.00246612
$732$		−	7.82717i		−	0.289300i
$733$		−	51.7037i		−	1.90972i	−0.297059	−	0.954859i	$-0.596006\pi$
$733$		−	51.7037i		−	1.90972i	0.297059	−	0.954859i	$-0.403994\pi$
$734$	27.1941			1.00375
$735$	5.15257	−	0.723926i	0.190055	−	0.0267024i
$736$	−4.21432			−0.155342
$737$		−	3.35260i		−	0.123494i
$738$			26.8020i			0.986594i
$739$	5.98079			0.220007			0.110003	−	0.993931i	$-0.464914\pi$
$739$	5.98079			0.220007			0.110003	+	0.993931i	$0.464914\pi$
$740$	4.47457	−	0.628669i	0.164489	−	0.0231103i
$741$	−29.5560			−1.08577
$742$		−	16.3225i		−	0.599217i
$743$			46.4880i			1.70548i	0.522337	+	0.852739i	$0.325060\pi$
$743$			46.4880i			1.70548i	−0.522337	+	0.852739i	$0.674940\pi$
$744$	2.50961			0.0920066
$745$	−1.84299	−	13.1175i	−0.0675219	−	0.480589i
$746$	0.214320			0.00784680
$747$			20.6811i			0.756680i
$748$			0.0142901i			0.000522498i
$749$	32.3067			1.18046
$750$	3.13182	+	7.03657i	0.114358	+	0.256939i
$751$	−3.25088			−0.118626			−0.0593132	−	0.998239i	$-0.518891\pi$
$751$	−3.25088			−0.118626			−0.0593132	+	0.998239i	$0.518891\pi$
$752$			7.59210i			0.276856i
$753$		−	18.1718i		−	0.662216i
$754$	3.21432			0.117059
$755$	−4.72393	−	33.6227i	−0.171921	−	1.22366i
$756$	7.24443			0.263477
$757$			28.2636i			1.02726i	0.858012	+	0.513630i	$0.171700\pi$
$757$			28.2636i			1.02726i	−0.858012	+	0.513630i	$0.828300\pi$
$758$			3.73329i			0.135599i
$759$	−0.622216			−0.0225850
$760$	−17.5002	+	2.45875i	−0.634800	+	0.0891883i
$761$	36.6766			1.32953			0.664763	−	0.747054i	$-0.268533\pi$
$761$	36.6766			1.32953			0.664763	+	0.747054i	$0.268533\pi$
$762$		−	4.72393i		−	0.171130i
$763$			18.0415i			0.653146i
$764$	1.17775			0.0426097
$765$	0.372862	−	0.0523864i	0.0134809	−	0.00189404i
$766$	−15.6035			−0.563777
$767$		−	12.1334i		−	0.438110i
$768$		−	0.688892i		−	0.0248583i
$769$	−3.63651			−0.131136			−0.0655679	−	0.997848i	$-0.520886\pi$
$769$	−3.63651			−0.131136			−0.0655679	+	0.997848i	$0.520886\pi$
$770$	−0.126900	−	0.903212i	−0.00457314	−	0.0325495i
$771$	−12.0810			−0.435085
$772$		−	8.23506i		−	0.296386i
$773$		−	28.9195i		−	1.04016i	−0.854117	−	0.520081i	$-0.825902\pi$
$773$		−	28.9195i		−	1.04016i	0.854117	−	0.520081i	$-0.174098\pi$
$774$	−2.52543			−0.0907746
$775$	−17.5096	+	5.01921i	−0.628964	+	0.180295i
$776$	−2.06668			−0.0741894
$777$		−	2.64941i		−	0.0950472i
$778$			36.1847i			1.29728i
$779$	−83.8756			−3.00515
$780$	1.16346	+	8.28100i	0.0416587	+	0.296507i
$781$	1.32201			0.0473051
$782$			0.280996i			0.0100484i
$783$			2.25380i			0.0805442i
$784$	3.37778			0.120635
$785$	17.1699	−	2.41234i	0.612821	−	0.0861002i
$786$	3.58120			0.127737
$787$			7.84944i			0.279802i	0.990165	+	0.139901i	$0.0446785\pi$
$787$			7.84944i			0.279802i	−0.990165	+	0.139901i	$0.955322\pi$
$788$		−	0.00492217i		−	0.000175345i
$789$	0.443985			0.0158063
$790$	6.49532	−	0.912580i	0.231093	−	0.0324681i
$791$	−3.46812			−0.123312
$792$			0.541249i			0.0192324i
$793$			61.6800i			2.19032i
$794$	−18.9032			−0.670850
$795$	1.83807	+	13.0825i	0.0651895	+	0.463988i
$796$	−22.4035			−0.794069
$797$			2.85236i			0.101036i	0.998723	+	0.0505178i	$0.0160872\pi$
$797$			2.85236i			0.101036i	−0.998723	+	0.0505178i	$0.983913\pi$
$798$			10.3620i			0.366810i
$799$	0.506215			0.0179086
$800$	1.37778	+	4.80642i	0.0487120	+	0.169933i
$801$	40.3071			1.42418
$802$			23.0098i			0.812506i
$803$			3.26962i			0.115382i
$804$	10.7763			0.380051
$805$	−2.49532	−	17.7605i	−0.0879483	−	0.625975i
$806$	−19.7763			−0.696591
$807$			18.4800i			0.650526i
$808$		−	7.60639i		−	0.267592i
$809$	−27.4429			−0.964842			−0.482421	−	0.875939i	$-0.660242\pi$
$809$	−27.4429			−0.964842			−0.482421	+	0.875939i	$0.660242\pi$
$810$	10.9699	−	1.54125i	0.385443	−	0.0541540i
$811$	−13.5906			−0.477230			−0.238615	−	0.971114i	$-0.576693\pi$
$811$	−13.5906			−0.477230			−0.238615	+	0.971114i	$0.576693\pi$
$812$		−	1.12690i		−	0.0395464i
$813$			17.6237i			0.618092i
$814$	0.433085			0.0151796
$815$	−24.4701	+	3.43801i	−0.857151	+	0.120428i
$816$	−0.0459330			−0.00160797
$817$		−	7.90321i		−	0.276498i
$818$		−	21.3669i		−	0.747076i
$819$	−26.0923			−0.911740
$820$	3.30174	+	23.5002i	0.115302	+	0.820664i
$821$	−11.2573			−0.392884			−0.196442	−	0.980515i	$-0.562939\pi$
$821$	−11.2573			−0.392884			−0.196442	+	0.980515i	$0.562939\pi$
$822$		−	9.16346i		−	0.319613i
$823$		−	21.9585i		−	0.765426i	−0.923867	−	0.382713i	$-0.874990\pi$
$823$		−	21.9585i		−	0.765426i	0.923867	−	0.382713i	$-0.125010\pi$
$824$	5.18421			0.180600
$825$	0.203420	+	0.709636i	0.00708219	+	0.0247063i
$826$	−4.25380			−0.148009
$827$		−	9.67154i		−	0.336312i	−0.985760	−	0.168156i	$-0.946219\pi$
$827$		−	9.67154i		−	0.336312i	0.985760	−	0.168156i	$-0.0537813\pi$
$828$			10.6430i			0.369868i
$829$	27.0020			0.937818			0.468909	−	0.883246i	$-0.344647\pi$
$829$	27.0020			0.937818			0.468909	+	0.883246i	$0.344647\pi$
$830$	2.54770	+	18.1334i	0.0884320	+	0.629418i
$831$	−7.74620			−0.268713
$832$			5.42864i			0.188204i
$833$		−	0.225219i		−	0.00780338i
$834$	5.68736			0.196937
$835$	14.4143	−	2.02519i	0.498829	−	0.0700846i
$836$	−1.69381			−0.0585818
$837$		−	13.8666i		−	0.479301i
$838$		−	11.6365i		−	0.401976i
$839$	−30.1497			−1.04088			−0.520441	−	0.853898i	$-0.674232\pi$
$839$	−30.1497			−1.04088			−0.520441	+	0.853898i	$0.674232\pi$
$840$	2.90321	−	0.407896i	0.100170	−	0.0140737i
$841$	−28.6494			−0.987911
$842$		−	24.3798i		−	0.840183i
$843$		−	14.2919i		−	0.492239i
$844$	21.3274			0.734120
$845$	−5.12399	−	36.4701i	−0.176270	−	1.25461i
$846$	19.1733			0.659192
$847$			20.8479i			0.716343i
$848$			8.57628i			0.294511i
$849$	2.63311			0.0903683
$850$	0.320476	−	0.0918659i	0.0109922	−	0.00315097i
$851$	8.51606			0.291927
$852$			4.24935i			0.145580i
$853$			23.2859i			0.797295i	0.917104	+	0.398647i	$0.130520\pi$
$853$			23.2859i			0.797295i	−0.917104	+	0.398647i	$0.869480\pi$
$854$	21.6242			0.739966
$855$	6.20940	+	44.1956i	0.212357	+	1.51146i
$856$	−16.9748			−0.580187
$857$		−	9.58766i		−	0.327508i	−0.986501	−	0.163754i	$-0.947640\pi$
$857$		−	9.58766i		−	0.327508i	0.986501	−	0.163754i	$-0.0523604\pi$
$858$			0.801502i			0.0273628i
$859$	22.4064			0.764495			0.382248	−	0.924060i	$-0.375150\pi$
$859$	22.4064			0.764495			0.382248	+	0.924060i	$0.375150\pi$
$860$	−2.21432	+	0.311108i	−0.0755077	+	0.0106087i
$861$	13.9146			0.474208
$862$			21.4050i			0.729057i
$863$		−	9.80198i		−	0.333663i	−0.985985	−	0.166832i	$-0.946646\pi$
$863$		−	9.80198i		−	0.333663i	0.985985	−	0.166832i	$-0.0533536\pi$
$864$	−3.80642			−0.129497
$865$	−3.88739	+	0.546171i	−0.132175	+	0.0185704i
$866$	19.8464			0.674407
$867$		−	11.7081i		−	0.397628i
$868$			6.93332i			0.235332i
$869$	0.628669			0.0213261
$870$	0.126900	+	0.903212i	0.00430230	+	0.0306218i
$871$	−84.9200			−2.87740
$872$		−	9.47949i		−	0.321016i
$873$			5.21924i			0.176645i
$874$	−33.3067			−1.12661
$875$	−19.4400	+	8.65233i	−0.657192	+	0.292502i
$876$	−10.5096			−0.355087
$877$			18.9862i			0.641118i	0.947229	+	0.320559i	$0.103871\pi$
$877$			18.9862i			0.641118i	−0.947229	+	0.320559i	$0.896129\pi$
$878$		−	34.5433i		−	1.16578i
$879$	16.4919			0.556259
$880$	0.0666765	+	0.474572i	0.00224767	+	0.0159978i
$881$	−34.5308			−1.16337			−0.581687	−	0.813413i	$-0.697607\pi$
$881$	−34.5308			−1.16337			−0.581687	+	0.813413i	$0.697607\pi$
$882$		−	8.53035i		−	0.287232i
$883$		−	0.904743i		−	0.0304470i	−0.999884	−	0.0152235i	$-0.995154\pi$
$883$		−	0.904743i		−	0.0304470i	0.999884	−	0.0152235i	$-0.00484598\pi$
$884$	0.361963			0.0121741
$885$	3.40943	−	0.479018i	0.114607	−	0.0161020i
$886$	−0.698260			−0.0234585
$887$			28.0192i			0.940793i	0.882455	+	0.470397i	$0.155889\pi$
$887$			28.0192i			0.940793i	−0.882455	+	0.470397i	$0.844111\pi$
$888$			1.39207i			0.0467150i
$889$	13.0509			0.437712
$890$	35.3417	−	4.96544i	1.18466	−	0.166442i
$891$	1.06175			0.0355701
$892$			15.9541i			0.534182i
$893$			60.0020i			2.00789i
$894$	4.08097			0.136488
$895$	−0.0113757	−	0.0809666i	−0.000380247	−	0.00270642i
$896$	1.90321			0.0635818
$897$			15.7605i			0.526227i
$898$		−	13.7955i		−	0.460363i
$899$	−2.15701			−0.0719403
$900$	12.1383	−	3.47949i	0.404609	−	0.115983i
$901$	0.571837			0.0190506
$902$			2.27454i			0.0757340i
$903$			1.31111i			0.0436309i
$904$	1.82225			0.0606070
$905$	−2.34767	−	16.7096i	−0.0780393	−	0.555447i
$906$	10.4603			0.347520
$907$		−	26.9418i		−	0.894587i	−0.894387	−	0.447294i	$-0.852388\pi$
$907$		−	26.9418i		−	0.894587i	0.894387	−	0.447294i	$-0.147612\pi$
$908$			15.7462i			0.522556i
$909$	−19.2094			−0.637135
$910$	−22.8780	+	3.21432i	−0.758399	+	0.106554i
$911$	−13.0859			−0.433555			−0.216777	−	0.976221i	$-0.569555\pi$
$911$	−13.0859			−0.433555			−0.216777	+	0.976221i	$0.569555\pi$
$912$		−	5.44446i		−	0.180284i
$913$			1.75509i			0.0580851i
$914$	−27.9813			−0.925538
$915$	−17.3319	+	2.43509i	−0.572973	+	0.0805017i
$916$	−1.00937			−0.0333505
$917$			9.89384i			0.326724i
$918$			0.253799i			0.00837662i
$919$	−45.3388			−1.49559			−0.747794	−	0.663931i	$-0.768887\pi$
$919$	−45.3388			−1.49559			−0.747794	+	0.663931i	$0.768887\pi$
$920$	1.31111	+	9.33185i	0.0432259	+	0.307662i
$921$	7.14473			0.235427
$922$		−	40.6671i		−	1.33930i
$923$		−	33.4859i		−	1.10220i
$924$	0.280996			0.00924410
$925$	−2.78415	−	9.71255i	−0.0915423	−	0.319347i
$926$	3.87463			0.127328
$927$		−	13.0923i		−	0.430009i
$928$			0.592104i			0.0194368i
$929$	1.69181			0.0555064			0.0277532	−	0.999615i	$-0.491165\pi$
$929$	1.69181			0.0555064			0.0277532	+	0.999615i	$0.491165\pi$
$930$	−0.780758	−	5.55707i	−0.0256021	−	0.182224i
$931$	26.6953			0.874905
$932$		−	5.29036i		−	0.173292i
$933$		−	16.4810i		−	0.539565i
$934$	−6.62867			−0.216897
$935$	0.0316429	−	0.00444576i	0.00103483	−	0.000145392i
$936$	13.7096			0.448113
$937$			46.2306i			1.51029i	0.655559	+	0.755144i	$0.272433\pi$
$937$			46.2306i			1.51029i	−0.655559	+	0.755144i	$0.727567\pi$
$938$			29.7719i			0.972086i
$939$	2.03164			0.0663002
$940$	16.8113	−	2.36196i	0.548326	−	0.0770387i
$941$	−54.8450			−1.78790			−0.893948	−	0.448171i	$-0.852076\pi$
$941$	−54.8450			−1.78790			−0.893948	+	0.448171i	$0.852076\pi$
$942$			5.34170i			0.174042i
$943$			44.7259i			1.45648i
$944$	2.23506			0.0727451
$945$	−2.25380	−	16.0415i	−0.0733161	−	0.521830i
$946$	−0.214320			−0.00696814
$947$		−	29.6974i		−	0.965034i	−0.875887	−	0.482517i	$-0.839723\pi$
$947$		−	29.6974i		−	0.965034i	0.875887	−	0.482517i	$-0.160277\pi$
$948$			2.02074i			0.0656307i
$949$	82.8183			2.68840
$950$	10.8889	+	37.9862i	0.353283	+	1.23243i
$951$	−6.03503			−0.195699
$952$		−	0.126900i		−	0.00411284i
$953$			27.3620i			0.886341i	0.896437	+	0.443170i	$0.146146\pi$
$953$			27.3620i			0.886341i	−0.896437	+	0.443170i	$0.853854\pi$
$954$	21.6588			0.701229
$955$	−0.366409	−	2.60793i	−0.0118567	−	0.0843905i
$956$	8.02567			0.259569
$957$			0.0874201i			0.00282589i
$958$		−	25.8894i		−	0.836448i
$959$	25.3160			0.817497
$960$	−1.52543	+	0.214320i	−0.0492330	+	0.00691714i
$961$	−17.7288			−0.571898
$962$		−	10.9699i		−	0.353683i
$963$			42.8687i			1.38142i
$964$	−15.3067			−0.492994
$965$	−18.2351	+	2.56199i	−0.587007	+	0.0824735i
$966$	5.52543			0.177778
$967$		−	7.18220i		−	0.230964i	−0.993310	−	0.115482i	$-0.963159\pi$
$967$		−	7.18220i		−	0.230964i	0.993310	−	0.115482i	$-0.0368413\pi$
$968$		−	10.9541i		−	0.352077i
$969$	−0.363018			−0.0116618
$970$	0.642959	+	4.57628i	0.0206442	+	0.146936i
$971$	−12.8365			−0.411944			−0.205972	−	0.978558i	$-0.566036\pi$
$971$	−12.8365			−0.411944			−0.205972	+	0.978558i	$0.566036\pi$
$972$			14.8321i			0.475739i
$973$			15.7126i			0.503721i
$974$	9.43017			0.302162
$975$	17.9748	−	5.15257i	0.575655	−	0.165014i
$976$	−11.3620			−0.363688
$977$			45.3495i			1.45086i	0.688296	+	0.725430i	$0.258359\pi$
$977$			45.3495i			1.45086i	−0.688296	+	0.725430i	$0.741641\pi$
$978$		−	7.61285i		−	0.243432i
$979$	3.42065			0.109325
$980$	−1.05086	−	7.47949i	−0.0335683	−	0.238924i
$981$	−23.9398			−0.764338
$982$			2.14764i			0.0685340i
$983$		−	22.8435i		−	0.728593i	−0.931283	−	0.364297i	$-0.881309\pi$
$983$		−	22.8435i		−	0.728593i	0.931283	−	0.364297i	$-0.118691\pi$
$984$	−7.31111			−0.233070
$985$	−0.0108993	+	0.00153133i	−0.000347279	+	4.87921e-5i
$986$	0.0394795			0.00125728
$987$		−	9.95407i		−	0.316841i
$988$			42.9037i			1.36495i
$989$	−4.21432			−0.134008
$990$	1.19850	−	0.168387i	0.0380908	−	0.00535168i
$991$	−30.4256			−0.966500			−0.483250	−	0.875482i	$-0.660544\pi$
$991$	−30.4256			−0.966500			−0.483250	+	0.875482i	$0.660544\pi$
$992$		−	3.64296i		−	0.115664i
$993$		−	9.74620i		−	0.309286i
$994$	−11.7397			−0.372362
$995$	6.96989	+	49.6084i	0.220960	+	1.57269i
$996$	−5.64143			−0.178755
$997$		−	27.4509i		−	0.869379i	−0.900580	−	0.434690i	$-0.856858\pi$
$997$		−	27.4509i		−	0.869379i	0.900580	−	0.434690i	$-0.143142\pi$
$998$			9.04593i			0.286344i
$999$	7.69181			0.243358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.b.a.259.2	✓	6
5.2	odd	4		2150.2.a.bd.1.2		3
5.3	odd	4		2150.2.a.bc.1.2		3
5.4	even	2	inner	430.2.b.a.259.5	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.b.a.259.2	✓	6	1.1	even	1	trivial
430.2.b.a.259.5	yes	6	5.4	even	2	inner
2150.2.a.bc.1.2		3	5.3	odd	4
2150.2.a.bd.1.2		3	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -0.688892i q^{3} -1.00000 q^{4} +(0.311108 + 2.21432i) q^{5} -0.688892 q^{6} -1.90321i q^{7} +1.00000i q^{8} +2.52543 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -0.688892i q^{3} -1.00000 q^{4} +(0.311108 + 2.21432i) q^{5} -0.688892 q^{6} -1.90321i q^{7} +1.00000i q^{8} +2.52543 q^{9} +(2.21432 - 0.311108i) q^{10} +0.214320 q^{11} +0.688892i q^{12} -5.42864i q^{13} -1.90321 q^{14} +(1.52543 - 0.214320i) q^{15} +1.00000 q^{16} -0.0666765i q^{17} -2.52543i q^{18} +7.90321 q^{19} +(-0.311108 - 2.21432i) q^{20} -1.31111 q^{21} -0.214320i q^{22} -4.21432i q^{23} +0.688892 q^{24} +(-4.80642 + 1.37778i) q^{25} -5.42864 q^{26} -3.80642i q^{27} +1.90321i q^{28} -0.592104 q^{29} +(-0.214320 - 1.52543i) q^{30} +3.64296 q^{31} -1.00000i q^{32} -0.147643i q^{33} -0.0666765 q^{34} +(4.21432 - 0.592104i) q^{35} -2.52543 q^{36} +2.02074i q^{37} -7.90321i q^{38} -3.73975 q^{39} +(-2.21432 + 0.311108i) q^{40} -10.6128 q^{41} +1.31111i q^{42} -1.00000i q^{43} -0.214320 q^{44} +(0.785680 + 5.59210i) q^{45} -4.21432 q^{46} +7.59210i q^{47} -0.688892i q^{48} +3.37778 q^{49} +(1.37778 + 4.80642i) q^{50} -0.0459330 q^{51} +5.42864i q^{52} +8.57628i q^{53} -3.80642 q^{54} +(0.0666765 + 0.474572i) q^{55} +1.90321 q^{56} -5.44446i q^{57} +0.592104i q^{58} +2.23506 q^{59} +(-1.52543 + 0.214320i) q^{60} -11.3620 q^{61} -3.64296i q^{62} -4.80642i q^{63} -1.00000 q^{64} +(12.0207 - 1.68889i) q^{65} -0.147643 q^{66} -15.6430i q^{67} +0.0666765i q^{68} -2.90321 q^{69} +(-0.592104 - 4.21432i) q^{70} +6.16839 q^{71} +2.52543i q^{72} +15.2558i q^{73} +2.02074 q^{74} +(0.949145 + 3.31111i) q^{75} -7.90321 q^{76} -0.407896i q^{77} +3.73975i q^{78} +2.93332 q^{79} +(0.311108 + 2.21432i) q^{80} +4.95407 q^{81} +10.6128i q^{82} +8.18913i q^{83} +1.31111 q^{84} +(0.147643 - 0.0207436i) q^{85} -1.00000 q^{86} +0.407896i q^{87} +0.214320i q^{88} +15.9605 q^{89} +(5.59210 - 0.785680i) q^{90} -10.3319 q^{91} +4.21432i q^{92} -2.50961i q^{93} +7.59210 q^{94} +(2.45875 + 17.5002i) q^{95} -0.688892 q^{96} +2.06668i q^{97} -3.37778i q^{98} +0.541249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9	\( 6 q - 6 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9} - 12 q^{11} + 2 q^{14} - 4 q^{15} + 6 q^{16} + 34 q^{19} - 2 q^{20} - 8 q^{21} + 4 q^{24} - 2 q^{25} - 6 q^{26} + 10 q^{29} + 12 q^{30} - 18 q^{31} + 12 q^{35} - 2 q^{36} + 4 q^{39} - 10 q^{41} + 12 q^{44} + 18 q^{45} - 12 q^{46} + 20 q^{49} + 8 q^{50} - 40 q^{51} + 4 q^{54} - 2 q^{56} - 40 q^{59} + 4 q^{60} - 42 q^{61} - 6 q^{64} + 32 q^{65} + 12 q^{66} - 4 q^{69} + 10 q^{70} - 16 q^{71} - 28 q^{74} + 32 q^{75} - 34 q^{76} + 18 q^{79} + 2 q^{80} - 10 q^{81} + 8 q^{84} - 12 q^{85} - 6 q^{86} + 28 q^{89} + 20 q^{90} - 22 q^{91} + 32 q^{94} + 2 q^{95} - 4 q^{96} + 16 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9 - 12 * q^11 + 2 * q^14 - 4 * q^15 + 6 * q^16 + 34 * q^19 - 2 * q^20 - 8 * q^21 + 4 * q^24 - 2 * q^25 - 6 * q^26 + 10 * q^29 + 12 * q^30 - 18 * q^31 + 12 * q^35 - 2 * q^36 + 4 * q^39 - 10 * q^41 + 12 * q^44 + 18 * q^45 - 12 * q^46 + 20 * q^49 + 8 * q^50 - 40 * q^51 + 4 * q^54 - 2 * q^56 - 40 * q^59 + 4 * q^60 - 42 * q^61 - 6 * q^64 + 32 * q^65 + 12 * q^66 - 4 * q^69 + 10 * q^70 - 16 * q^71 - 28 * q^74 + 32 * q^75 - 34 * q^76 + 18 * q^79 + 2 * q^80 - 10 * q^81 + 8 * q^84 - 12 * q^85 - 6 * q^86 + 28 * q^89 + 20 * q^90 - 22 * q^91 + 32 * q^94 + 2 * q^95 - 4 * q^96 + 16 * q^99

Introduction

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